Predicting pillar stability for underground mine using Fisher discriminant analysis and SVM methods

The purpose of this study is to apply some statistical and soft computing methods such as Fisher discriminant analysis （FDA） and support vector machines （SVMs） methodology to the determination of pillar stability for underground mines selected from various coal and stone mines by using some index and mechanical properties, including the width, the height, the ratio of the pillar width to its height, the uniaxial compressive strength of the rock and pillar stress. The study includes four main stages： sampling, testing, modeling and assessment of the model performances. During the modeling stage, two pillar stability prediction models were investigated with FDA and SVMs methodology based on the statistical learning theory. After using 40 sets of measured data in various mines in the world for training and testing, the model was applied to other 6 data for validating the trained proposed models. The prediction results of SVMs were compared with those of FDA as well as the measured field values. The general performance of models developed in this study is close; however, the SVMs exhibit the best performance considering the performance index with the correct classification rate Prs by re-substitution method and Pcv by cross validation method. The results show that the SVMs approach has the potential to be a reliable and practical tool for determination of pillar stability for underground mines.

On-line Batch Process Monitoring and Diagnosing Based on Fisher Discriminant Analysis

A new on-line batch process monitoring and diagnosing approach based on Fisher discriminant analysis （FDA） was proposed. This method does not need to predict the future observations of variables, so it is more sensitive to fault detection and stronger implement for monitoring. In order to improve the monitoring performance, the variables trajectories of batch process are separated into several blocks. The key to the proposed approach for on-line monitoring is to calculate the distance of block data that project to low-dimension Fisher space between new batch and reference batch. Comparing the distance with the predefine threshold, it can be considered whether the batch process is normal or abnormal. Fault diagnosis is performed based on the weights in fault direction calculated by FDA. The proposed method was applied to the simulation model of fed-batch penicillin fermentation and the resuits were compared with those obtained using MPCA. The simulation results clearly show that the on-line monitoring method based on FDA is more efficient than the MPCA.

Analysis and Experiments on Two Linear Discriminant Analysis Methods

Foley-Sammon linear discriminant analysis (FSLDA) and uncorrelated linear discriminant analysis (ULDA) are two well-known kinds of linear discriminant analysis. Both ULDA and FSLDA search the kth discriminant vector in an n-k+1 dimensional subspace, while they are subject to their respective constraints. Evidenced by strict demonstration, it is clear that in essence ULDA vectors are the covariance-orthogonal vectors of the corresponding eigen-equation. So, the algorithms for the covariance-orthogonal vectors are equivalent to the original algorithm of ULDA, which is time-consuming. Also, it is first revealed that the Fisher criterion value of each FSLDA vector must be not less than that of the corresponding ULDA vector by theory analysis. For a discriminant vector, the larger its Fisher criterion value is, the more powerful in discriminability it is. So, for FSLDA vectors, corresponding to larger Fisher criterion values is an advantage. On the other hand, in general any two feature components extracted by FSLDA vectors are statistically correlated with each other, which may make the discriminant vectors set at a disadvantageous position. In contrast to FSLDA vectors, any two feature components extracted by ULDA vectors are statistically uncorrelated with each other. Two experiments on CENPARMI handwritten numeral database and ORL database are performed. The experimental results are consistent with the theory analysis on Fisher criterion values of ULDA vectors and FSLDA vectors. The experiments also show that the equivalent algorithm of ULDA, presented in this paper, is much more efficient than the original algorithm of ULDA, as the theory analysis expects. Moreover, it appears that if there is high statistical correlation between feature components extracted by FSLDA vectors, FSLDA will not perform well, in spite of larger Fisher criterion value owned by every FSLDA vector. However, when the average correlation coefficient of feature components extracted by FSLDA vectors is at a low level, the performance of FSLDA are comparable with ULDA.

A computer aided detection framework for mammographic images using fisher linear discriminant and nearest neighbor classifier

Today, mammography is the best method for early detection of breast cancer. Radiologists failed to detect evident cancerous signs in approximately 20% of false negative mammograms. False negatives have been identified as the inability of the radiologist to detect the abnormalities due to several reasons such as poor image quality, image noise, or eye fatigue. This paper presents a framework for a computer aided detection system that integrates Principal Component Analysis (PCA), Fisher Linear Discriminant (FLD), and Nearest Neighbor Classifier (KNN) algorithms for the detection of abnormalities in mammograms. Using normal and abnormal mammograms from the MIAS database, the integrated algorithm achieved 93.06% classification accuracy. Also in this paper, we present an analysis of the integrated algorithm’s parameters and suggest selection criteria.

An Optimization Criterion for Generalized Marginal Fisher Analysis on Undersampled Problems

Marginal Fisher analysis （MFA） not only aims to maintain the original relations of neighboring data points of the same class but also wants to keep away neighboring data points of the different classes.MFA can effectively overcome the limitation of linear discriminant analysis （LDA） due to data distribution assumption and available projection directions.However,MFA confronts the undersampled problems.Generalized marginal Fisher analysis （GMFA） based on a new optimization criterion is presented,which is applicable to the undersampled problems.The solutions to the proposed criterion for GMFA are derived,which can be characterized in a closed form.Among the solutions,two specific algorithms,namely,normal MFA （NMFA） and orthogonal MFA （OMFA）,are studied,and the methods to implement NMFA and OMFA are proposed.A comparative study on the undersampled problem of face recognition is conducted to evaluate NMFA and OMFA in terms of classification accuracy,which demonstrates the effectiveness of the proposed algorithms.

Multispectral Imaging in Combination with Multivariate Analysis Discriminates Selenite Induced Cataractous Lenses from Healthy Lenses of Sprague-Dawley Rats

Cataracts are the leading cause of blindness worldwide. Current methods for discriminating cataractous lenses from healthy lenses of Sprague-Dawley rats during preclinical studies are based on either histopathological or clinical assessments which are weakened by subjectivity. In this work, both cataractous and healthy lens tissues of Sprague-Dawley rats were studied using multispectral imaging technique in combination with multivariate analysis. Multispectral images were captured in transmission, reflection and scattering modes. In all, five spectral bands were found to be markers for discriminating cataractous lenses from healthy lenses;470 nm and 625 nm discriminated in reflection mode whereas 435 nm, 590 nm and 700 nm discriminated in transmission mode. With Fisher’s Linear discriminant analysis, the midpoints for classifying cataractous from healthy lenses were found to be 14.718 × 10−14 and 3.2374 × 10−14 for the two spectra bands in the reflection mode and the three spectral bands in the transmission mode respectively. Images in scattering mode did not show significant discrimination. These spectral bands in reflection and transmission modes may offer potential diagnostic markers for discriminating cataractous lenses from healthy lenses thereby promising multispectral imaging applications for characterizing cataractous and healthy lenses.

DISCRIMINATIVE ANALYSIS OF FUNCTIONAL NEAR-INFRARED SPECTROSCOPY SIGNALS FOR DEVELOPMENT OF NEUROIMAGING BIOMARKERS OF ELDERLY DEPRESSION

Functional near-infrared spectroscopy(fNIRS)is a neuroimaging technology which is suitable for psychiatric patients.Several fNIRS studies have found abnormal brain activations during cognitive tasks in elderly depression.In this paper,we proposed a discriminative model of multivariate pattern classification based on fNIRS signals to distinguish elderly depressed patients from healthy controls.This model used the brain activation patterns during a verbal fluency task as features of classification.Then Pseudo-Fisher Linear Discriminant Analysis was performed on the feature space to generate discriminative model.Using leave-one-out(LOO)cross-validation,our results showed a correct classification rate of 88%.The discriminative model showed its ability to identify people with elderly depression and suggested that fNIRS may be an efficient clinical tool for diagnosis of depression.This study may provide the first step for the development of neuroimaging biomarkers based on fNIRS in psychiatric disorders.

BOOTSTRAP TECHNIQUE FOR ROC ANALYSIS: A STABLE EVALUATION OF FISHER CLASSIFIER PERFORMANCE

This paper presents a novel bootstrap based method for Receiver Operating Characteristic (ROC) analysis of Fisher classifier. By defining Fisher classifier’s output as a statistic, the bootstrap technique is used to obtain the sampling distributions of the outputs for the positive class and the negative class respectively. As a result, the ROC curve is a plot of all the (False Positive Rate (FPR), True Positive Rate (TPR)) pairs by varying the decision threshold over the whole range of the boot- strap sampling distributions. The advantage of this method is, the bootstrap based ROC curves are much stable than those of the holdout or cross-validation, indicating a more stable ROC analysis of Fisher classifier. Experiments on five data sets publicly available demonstrate the effectiveness of the proposed method.

Texture Analysis and Characteristic Identification About Plaque Tissues of IVUS

Intravascular ultrasound can provide clear real-time cross-sectional images,including lumen and plaque.In practice,to identify the plaques tissues in different pathological changes is very important.However,the grayscale differences of them are not so apparent.In this paper a new textural characteristic space vector was formed by the combination of Co-occurrence Matrix and fraction methods.The vector was projected to the new characteristic space after multiplied by a projective matrix which can best classify those plaques according to the Fisher linear discriminant.Then the classification was completed in the new vector space.Experimental results found that the veracity of this classification could reach up to 88%,which would be an accessorial tool for doctors to identify each plaque.

基于Fisher判别法岩溶塌陷倾向性等级分类预测

为准确预测岩溶塌陷倾向性的等级分类,通过分析大量观测实例,选取岩性系数、岩体结构系数、地下水系数、覆盖层系数、地形地貌系数和环境条件系数作为模型判别因素。对12个实际观测样本进行训练,建立了基于Fisher判别分析法(FDA)的岩溶塌陷倾向性等级分类预测模型。借助SPSS软件工具,得到判别模型的4个判别函数。根据判别函数对训练样本进行回判,并对2个待判样本进行预测。结果显示:第一、第二判别函数的综合判别效率达到100%,大于规定的85%,满足工程实际应用需求;对训练样本进行回判时,误判率为零,同时对待判样本的分类预测准确率为100%。

露天采矿爆破振动对砌体结构破坏效应预测的Fisher判别模型及应用

应用Fisher判别分析理论并结合工程实际特点,从爆破振动特征参量和砌体结构自身特性这2个方面出发,选取峰值质点振动速度(PPV)、爆破振动主频率、主频率持续时间、灰缝强度、圈梁构造柱、房屋高度、屋盖形式和砖墙面积率8个影响因素作为判别因子,建立爆破振动对砌体结构破坏效应预测的Fisher判别分析模型。将该方法应用到湖北一露天采场爆破振动对砌体结构破坏效应预测问题中,利用现场实测的108组数据进行训练和检验,回判估计的误判率为0.083,通过求解判别函数,认为峰值质点振动速度为最重要的判别指标,其后依次为圈梁构造柱、屋盖形式、砖墙面积率、房屋高度、爆破振动主频率、主频率持续时间和灰缝强度,可以为同类工程在选取爆破振动对砌体结构破坏效应的判别指标方面提供参考。利用其他12组现场数据作为预测样本进行测试,预测结果与实际情况吻合较好。研究表明,该方法回判估计的误判率低,判别性能良好,是爆破振动对砌体结构破坏效应预测的一种有效新方法,可以在实际工程中进行推广应用。

用Fisher判别法确定矿井突水水源

运用Fisher判别分析(FDA)理论,根据含水层的标型组分和涌水点水样的化学成分,针对简单的两类和复杂的多类突(涌)水水源识别,分别建立Fisher的线性判别函数模型和典则判别的函数模型,并对它们进行判别分析,将所建的矿井突(涌)水水源识别的Fisher判别模型应用于华北某矿井予以验证。研究结果表明:该模型利用回代估计法所得到的误判率小,并具有较强的判别能力。运用该模型进行判别分析,简易方便,分类效率高,对研究矿井突(涌)水水源的快速、有效判别意义明显;该模型适用性强,有广阔的应用前景。

Fisher线性鉴别分析的理论研究及其应用

Fisher线性鉴别分析已成为特征抽取的最为有效的方法之一 .但是在高维、小样本情况下如何抽取Fisher最优鉴别特征仍是一个困难的、至今没有彻底解决的问题 .文中引入压缩映射和同构映射的思想 ,从理论上巧妙地解决了高维、奇异情况下最优鉴别矢量集的求解问题 ,而且该方法求解最优鉴别矢量集的全过程只需要在一个低维的变换空间内进行 ,这与传统方法相比极大地降低了计算量 .在此理论基础上 ,进一步为高维、小样本情况下的最优鉴别分析方法建立了一个通用的算法框架 ,即先作K L变换 ,再用Fisher鉴别变换作二次特征抽取 .基于该算法框架 ,提出了组合线性鉴别法 ,该方法综合利用了F S鉴别和J Y鉴别的优点 ,同时消除了二者的弱点 .在ORL标准人脸库上的试验表明 ,组合鉴别法所抽取的特征在普通的最小距离分类器和最近邻分类器下均达到 97%的正确识别率 ,而且识别结果十分稳定 .

砂土液化预测的Fisher判别模型及应用

基于Fisher判别理论建立了砂土液化可能性的Fisher判别分析(FDA)模型。在分析砂土液化影响因素的基础上,选取烈度、震中距、地下水位、砂层埋深、标贯击数、平均粒径、不均匀系数、剪应力比等8个实测特征指标作为FDA模型的预测指标。利用砂土液化的实测数据作为训练样本进行训练,建立FDA模型对砂土液化进行预测,并用其他未参加训练的实测数据进行了验证。研究结果表明,FDA模型简便可行、预测精度高,是解决砂土液化预测问题的有效方法之一。

冲击地压危险性等级预测的Fisher判别分析方法

应用统计学理论并结合工程实际,选取影响冲击地压的主要因素如煤厚、倾角、埋深、构造情况、倾角变化、煤厚变化、瓦斯浓度、顶板管理、卸压、响煤炮声作为判别因子,建立冲击地压危险性分级预测的Fisher判别分析模型(FDA)。利用重庆砚石台煤矿23组实测数据作为学习样本进行训练和检验,建立相应线性判别函数并利用回代估计方法进行回检,误判率为0。利用该模型其他12组现场数据作为预测样本进行测试,预测结果与实际情况吻合较好。

基于YCbCr颜色空间和Fisher判别分析的棉花图像分割研究

棉花的分割是采棉机器人研究的关键技术。本文分别在HSV、HIS和YCbCr颜色空间下,首先根据棉花的颜色信息与背景颜色信息的差距,对样本图像中的各个对象(棉絮、棉枝、土壤等)分类;其次根据分类结果分别提取各类在各颜色空间下的样本像素值;再根据类间离散度最大和类内离散度最小的准则计算出Fisher判别向量和各类的质心;最后按照像素值离各质心最近的准则进行图像分割。结果表明,在YCbCr颜色空间下产生的分割噪声最小,选取此颜色空间,采用贴标签的方法自适应去噪。实验仿真表明,本方法可有效避免阳光直射和阴影的干扰,对各种情况都能准确分割,分割准确率达90.44%。

隧道施工现场安全评价的费歇判别分析(FDA)模型及其应用

建立了隧道施工现场安全评价的费歇判别分析(FDA)模型,从基坑支护、施工用电、机械设备、安全管理等方面选取20个影响因素作为该模型的评判因子。充分利用隧道施工已有安全信息,根据工程施工的历史实例数据对FDA模型进行训练,将所建立的模型应用到某公司隧道施工的评价实例中。结果表明:评价结果和实际情况吻合;可以为隧道的安全施工提供理论指导,具有重要的实用价值,可在工程中推广使用;该评价方法也为隧道施工现场的安全评价提供了一条新的思路。

基于Fisher线性判别分析的语音信号端点检测方法

传统的语音端点检测方法对辅音,特别是受到噪声污染的清音部分与背景噪声之间分离能力不足。针对上述问题,该文提出一种基于Fisher线性判别分析的梅尔频率倒谱系数(F-MFCC)端点检测方法。将清音信号和背景噪声视为两类分类问题,采用Fisher准则求解具有判别信息的最佳投影方向,使得投影后的特征参数具有最小类内散度和最大类间散度,从而增大清音与背景噪声的可分离性。在不同语音库上的实验结果表明,F-MFCC能够在不同信噪比和背景噪声条件下提高语音端点检测的准确率。

基于排列组合熵和加权核Fisher的肌电跌倒检测

为实现老年人的跌倒与日常行为动作的模式识别,提出了一种基于排列组合熵和加权核Fisher线性判别的表面肌电信号跌倒识别方法.以腓肠肌和股外侧肌2路肌电信号对应的排列组合熵为特征向量输入加权核Fisher线性分类器进行模式识别,对跌倒与坐下、蹲下和行走进行识别.实验结果表明,该方法的跌倒识别率为93.33%,特异度100%,优于其他分类方法.